What Captain Black did was find parametric equations such that at the point (0, 3) and at the point (4, 0). "Three fifths of the way from (4, 0) to (0, 3)" is 1- 3/5= 2/5 of the way from (0, 3) to (4, 0).

I think I would have been inclined to do it the other way: find parametric equations such that gives the point (4, 0), and gives the point (0, 3). That way, "three fifths of the way from (4, 0) to (0, 3)" would be simply . Of course, to do that you would use the vector <0- 4, 3- 0>= <-4, 3> as the "direction vector".